As long as you don't set foot on British soil you'll be fine. But that's less simple than it sounds. Don't book a flight that connects in the UK, sure. But what if your NYC-to-Munich flight has engine trouble and needs to make an emergency landing in London? You are screwed: You'll be pulled off the plane and taken to jail.
Will the US embassy get involved? Of course. Will they get you released? Maybe, but it's not guaranteed. And you are in for a bad time regardless.
The UK knows their place. They could do that but they won't. Also, they'll have trouble even finding who the business operator is. The US allows pseudonymous business structures and their subpoena request will be thrown out on a 1st amendment defense.
I can only imagine the storm that would emerge if the morning the UK ever attempted to arrest an American for self-expression inside or outside the USA. That is how you get some Democracy delivered.
Will the US embassy get involved? Of course. Will they get you released? Maybe, but it's not guaranteed. And you are in for a bad time regardless.